Levenberg-Marquardt Training Algorithm Research Articles

A Comparative Analysis of the Bayesian Regularization and Levenberg–Marquardt Training Algorithms in Neural Networks for Small Datasets: A Metrics Prediction of Neolithic Laminar Artefacts

This study aims to present a comparative analysis of the Bayesian regularization backpropagation and Levenberg–Marquardt training algorithms in neural networks for the metrics prediction of damaged archaeological artifacts, of which the state of conservation is often fragmented due to different reasons, such as ritual, use wear, or post-depositional processes. The archaeological artifacts, specifically laminar blanks (so-called blades), come from different sites located in the Southern Levant that belong to the Pre-Pottery B Neolithic (PPNB) (10,100/9500–400 cal B.P.). This paper shows the entire procedure of the analysis, from its normalization of the dataset to its comparative analysis and overfitting problem resolution.

Prediction of pressure evolution in non-venting self-pressurized liquid hydrogen tanks using artificial neural network approach

Liquid hydrogen (LH2) is a future energy carrier compared to most conventional fuels. One of the practical bottlenecks in non-venting LH2 tanks is to accurately predict the pressure evolution. Accordingly, many thermal models and correlations were developed; however significant deviations arose due to inherent complex thermal phenomena which have not been addressed yet. A general artificial neural network (ANN) model has been first developed based on 448 datasets amassed from different literature sources to predict the pressure evolution under different heat fluxes, initial filling ratios, as well as tank volumes and shapes. The model has been configured with a typical multi-layer feed-forward structure using a back-propagation learning algorithm and Levenberg-Marquardt training algorithm. For the ANN model, a preliminary optimization process has been conducted for reaching the optimal values for training-to-testing datasets ratio, learning parameters and optimum network structure. Besides, some criteria were set to evaluate the ANN model performance. The ANN model with the configuration of 5-11-11-1 was found to be adopted for such a prediction task. Compared to experimental results and literature models and correlations, the ANN model has been proven to predict the pressure evolution in non-venting self-pressurized LH2 tanks with a mean square error of 1.1779 × 10−5 s2, root mean square error of 0.0034 s, mean absolute error of 6%, mean relative error of 0.2% as well as a satisfactory correlation coefficient of 0.99934 between the network outputs and corresponding targets. This research work provides an effective modeling approach based on artificial neural network to solve one complex problem related with LH2 tanks with fast, accurate and consistent results. Also, the results of the present work can offer some practical guidance for the design of LH2 tanks. Further, the present work gives some insights into new application areas of ANN which will be the emphasis of future research work.

Improving pressure drop predictions for R134a evaporation in corrugated vertical tubes using a machine learning technique trained with the Levenberg–Marquardt method

AbstractThe present investigation utilized a machine learning structure to ascertain the pressure drop in vertically positioned, corrugated copper tubes during the evaporation process of R134a. The evaporator was a counter-flow heat exchanger, in which R134a flowed in the inner corrugated tube and hot water flowed in the smooth annulus. Different evaporation mass fluxes (195–406 kg m-2 s-1) and heat fluxes (10.16–66.61 kW m-2) were used with artificial neural networks at different corrugation depths. A multilayer perceptron artificial neural network model with 13 neurons in the hidden layer was proposed. Tan-Sig and Purelin transfer functions were used in the network model developed with the Levenberg–Marquardt training algorithm. The dataset, which consisted of 252 data points, related to the evaporation process, was divided into training (70%), validation (15%), and testing (15%) groups in an arbitrary manner. The artificial neural network model has been demonstrated to effectively forecast the pressure drop that occurs during evaporation. The mean squared error was computed for the ΔP values observed during the evaporation processes, yielding a value of 1.96E-03. The artificial neural network exhibited a high correlation coefficient value of 0.94479. The estimation fluctuations exhibited a range of ± 10%, whereas the experimental and anticipated ΔP data demonstrated a divergence of ± 10.3%.

Investigating the effect of textural properties on CO2 adsorption in porous carbons via deep neural networks using various training algorithms

The adsorption of carbon dioxide (CO2) on porous carbon materials offers a promising avenue for cost-effective CO2 emissions mitigation. This study investigates the impact of textural properties, particularly micropores, on CO2 adsorption capacity. Multilayer perceptron (MLP) neural networks were employed and trained with various algorithms to simulate CO2 adsorption. Study findings reveal that the Levenberg–Marquardt (LM) algorithm excels with a remarkable mean squared error (MSE) of 2.6293E−5, indicating its superior accuracy. Efficiency analysis demonstrates that the scaled conjugate gradient (SCG) algorithm boasts the shortest runtime, while the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm requires the longest. The LM algorithm also converges with the fewest epochs, highlighting its efficiency. Furthermore, optimization identifies an optimal radial basis function (RBF) network configuration with nine neurons in the hidden layer and an MSE of 9.840E−5. Evaluation with new data points shows that the MLP network using the LM and bayesian regularization (BR) algorithms achieves the highest accuracy. This research underscores the potential of MLP deep neural networks with the LM and BR training algorithms for process simulation and provides insights into the pressure-dependent behavior of CO2 adsorption. These findings contribute to our understanding of CO2 adsorption processes and offer valuable insights for predicting gas adsorption behavior, especially in scenarios where micropores dominate at lower pressures and mesopores at higher pressures.

Predicting Earth-Vas2 parameters of coastal plain sand aquifers using artificial neural Network(s), in the Calabar region of Nigeria

This study employs artificial neural networks (ANNs), specifically the Nonlinear Autoregressive with External Input (NARX) model as an ANN add-on for Matlab, to forecast Earth-Vas2 parameters. The model leverages a time series approach, with the Earth-Vas2 index (y(t)) as the predictive target and various parameters (elevations, static water level, aquifer material thickness, transmissivity, hydraulic conductivity, specific capacity, vadose media) denoted as x(t) to facilitate accurate predictions. The Levenberg-Marquardt training algorithm was applied to the ANN using geo-hydraulic data from 56 boreholes for training and 24 boreholes for validation and testing. Validation metrics such as mean square error (MSE), correlation coefficient (R), and coefficient of determination (R2) were utilized. The results indicate a high degree of accuracy, with low MSE values of 0.0171 (training), 0.0087 (validation), and 0.0327 (testing). Strong correlation coefficients (R) of 0.9882, 0.9898, and 0.9844, along with high R2 values (97.66%), emphasize the robustness of the ANN model. Actual and predicted Earth-Vas2 values exhibit a similar pattern, affirming the model's effectiveness. The R-value of 0.9882 signifies a strong positive correlation within the model, validating its ability to capture variable interactions in fluid migration control. Geo-hydraulic Earth-Vas2 maps identify areas with varying migration efficiency, guiding groundwater management. The study emphasizes routine subsurface assessments for crucial data in environmental planning and risk reduction in industrial and municipal activities. This method provides cost-effective estimation of key geo-hydraulic properties for aquifer vulnerability assessments, with far-reaching implications for groundwater management, environmental protection, and land use planning.

Artificial neural Network-Based LCOH estimation for concentrated solar power plants for industrial process heating applications

A study was condacted to assess the feasibility of a 5MWt solar-only parabolic trough concentrated solar power (CSP) for industrial process heat (IPH) in various locations across Morocco. Furthermore, the initial plant design has been optimized by considering the number of full-load storage hours and the size of the solar field. Additionally, this study employs a Multi-Layer Perceptron (MLP) model, featuring five input parameters(storage hours, solar multiples,Direct Normal Irradiation, latitude, and longitude), two hidden layers, and one output parameter(levelized cost of heat (LCOH)). The model has been trained using Levenberg-Marquardt (LM) training algorithms. According to the study, the Errachidia site was found to be the most efficient location, generating 21983.56 MWhth at a LCOH of 3.31 ¢/kWth for the initial design. The optimal plant design was determined to have a solar multiple of 1.5 across all investigated sites. The statistical analysis revealed that the MLP model proposed in the study, which had 43 neurons in the hidden layer, demonstrates the lowest errors, including the root mean square error (0.0071) and the coefficient of variance (0.1852), and achieved the highest coefficient of determination value (0.99999) during the training process. Furthermore, the disparities in LCOH values between simulated data and the proposed MLP model across six different Moroccan cities, with errors ranging from 0.01% to −4.07%, confirm the reliability of the MLP model for predicting LCOH.

Defining the optimal conditions using FFNNs and NARX neural networks for modelling the extraction of Sc from aqueous solution by Cryptand-2.2.1 and Cryptand-2.1.1

The main aim of this study is to figure out how well cryptand-2.2.1 (C 2.2.1) and cryptand-2.1.1 (C 2.1.1) macrocyclic compounds (MCs) work as novel extractants for scandium (Sc) by using an artificial neural network (ANN) models in MATLAB software. Moreover, C2.2.1 and C2.1.1 have never been evaluated to recover Sc. The independent variables impacting the extraction process (concentration of MC, concentration of Sc, pH, and time), and a nonlinear autoregressive network with exogenous input (NARX) and feed-forward neural network (FFNN) models were used to estimate their optimum values. The greatest obstacle in the selective recovery process of the REEs is the similarity in their physicochemical properties, specifically their ionic radius. The recovery of Sc from the aqueous solution was experimentally evaluated, then the non-linear relationship between those parameters was predictively modeled using (NARX) and (FFNN). To confirm the extraction and stripping efficiency, an atomic absorption spectrophotometer (AAS) was employed. The results of the extraction investigations show that, for the best conditions of 0.008 mol/L MC concentration, 10 min of contact time, pH 2 of the aqueous solution, and 75 mg/L Sc initial concentration, respectively, the C 2.1.1 and C 2.2.1 extractants may reach 99 % of Sc extraction efficiency. Sc was recovered from a multi-element solution of scandium (Sc), yttrium (Y), and lanthanum (La) under these circumstances. Whereas, at a concentration of 0.3 mol/L of hydrochloric acid, the extraction of Sc was 99 %, as opposed to Y 10 % and La 7 %. The Levenberg-Marquardt training algorithm had the best training performance with an mean-squared-error, MSE, of 5.232x10−6 and 6.1387x10−5 for C 2.2.1 and C 2.1.1 respectively. The optimized FFNN architecture of 4-10-1 was constructed for modeling recovery of Sc. The extraction process was well modeled by the FFNN with an R2 of 0.999 for the two MC, indicating that the observed Sc recovery efficiency consistent with the predicted one.

An Artificial Neural Network for Predicting Groundnut Yield Using Climatic Data

Groundnut, being a widely consumed oily seed with significant health benefits and appealing sensory profiles, is extensively cultivated in tropical regions worldwide. However, the yield is substantially impacted by the changing climate. Therefore, predicting stressed groundnut yield based on climatic factors is desirable. This research focuses on predicting groundnut yield based on several combinations of climatic factors using artificial neural networks and three training algorithms. The Levenberg–Marquardt, Bayesian Regularization, and Scaled Conjugate Gradient algorithms were evaluated for their performance using climatic factors such as minimum temperature, maximum temperature, and rainfall in different regions of Sri Lanka, considering the seasonal variations in groundnut yield. A three-layer neural network was employed, comprising a hidden layer. The hidden layer consisted of 10 neurons, and the log sigmoid functions were used as the activation function. The performance of these configurations was evaluated based on the mean squared error and Pearson correlation. Notable improvements were observed when using the Levenberg–Marquardt algorithm as the training algorithm and applying the natural logarithm transformation to the yield values. These improvements were evident through the higher Pearson correlation values for training (0.84), validation (1.00) and testing (1.00), and a lower mean squared error (2.2859 × 10−21) value. Due to the limited data, K-Fold cross-validation was utilized for optimization, with a K value of 5 utilized for the process. The application of the natural logarithm transformation to the yield values resulted in a lower mean squared error (0.3724) value. The results revealed that the Levenberg–Marquardt training algorithm performs better in capturing the relationships between the climatic factors and groundnut yield. This research provides valuable insights into the utilization of climatic factors for predicting groundnut yield, highlighting the effectiveness of the training algorithms and emphasizing the importance of carefully selecting and expanding the climatic factors in the modeling equation.

Crashworthiness behavior assessment and multi-objective optimization of horsetail-inspired sandwich tubes based on artificial neural network

The crashworthiness behavior of horsetail-inspired sandwich tubes was analyzed in this study. Multilayer perceptron (MLP) algorithms with the Levenberg-Marquardt training algorithm (LMA) were used to predict force-displacement curve and optimize the geometrical parameters according to minimum peak crushing force and specific energy absorption. Based on the non-dominated sorting genetic algorithm II (NSGA-II) optimization results, the specimen with four core tubes and a thickness of 1 mm, and a height of 92 mm has the optimal crashworthiness performance. Finally, the optimal specimen is fabricated and the results of the numerical and MLP methods are validated versus experimental approach.

Artificial neural network accomplished prediction on tribology – A promising procedure to facilitate the tribological characterization of polymer composites

The aim of our investigations was to develop an artificial neural network (ANN) to reliably describe the pv dependence of different hybrid materials with identical basic components but different quantity ratios, and ultimately to explore whether it is possible to predict the effect of different component ratios on the tribological behavior on the basis of a limited number of experiments. For this purpose, the pressure (p) and velocity (v) dependence for five PEEK-based compounds systematically modified in their composition was investigated at different load levels on a block-on-ring tribometer. In parallel, an ANN was designed and optimized using Bayesian optimization. The results of four out of this five materials was used to train a ANN, whereas the Levenberg-Marquardt training algorithm was used as a kernel. This allowed us to describe the pv dependence of friction and wear of these materials in a fine-grained manner and thus evaluate their suitability under different operating conditions. The procedure was performed twice with four different materials.The experimental results of the fifth material in each case, which was not used for training, show very good agreement with the friction and wear properties predicted by the artificial neural network. It is thus shown that the combination of comparatively few experiments and ANN simulations enables a reliable and fine-mesh prediction of the friction and wear behavior of materials in a wide pv load range. Ultimately, the proportions of material components for different pv load ranges can thus be optimized by simulation, which would not be possible in experiments due to time and cost constraints. The comparative evaluation of different materials can be illustrated clearly in so-called tribomaps.

Modeling the effect of meteorological variables on streamflow estimation: application of data mining techniques in mixed rainfall-snowmelt regime Munzur River, Türkiye.

Revealing the dynamic link between rainfall and runoff, which are the main components of the hydrological cycle, is significant for the planning and managing water resources, disaster risk management, and construction of water structures. This study used feed-forward neural network (FFNN), adaptive neuro-fuzzy inference system (ANFIS), and long short-term memory (LSTM) network to model the rainfall-runoff relationship. Various variations of lagged precipitation, temperature, relative humidity, and flows were presented as inputs, and the flow values of Munzur River were estimated as outputs. During the selection of input parameters, variables with high correlation to flow values were utilized. The model's success was tested using several statistical indicators, including the coefficient of correlation (R), coefficient of determination (R2), and root mean square error (RMSE). When measuring values and model results are compared, FFNN and ANFIS models show accurate predictive results with high accuracy, while LSTM prediction results are not satisfactory. However, it was concluded that the FFNN model with the hyperbolic tangent sigmoid transfer function and Levenberg-Marquardt training algorithm made a slightly more accurate estimation. In addition, it was revealed that the best ANFIS-Sugeno model was obtained with a hybrid learning algorithm, Gaussmf membership function, and eight subsets. As a result of the analysis, it has been found that FFNN is superior to ANFIS in flow prediction. These results provide policymakers and planners with helpful information for developing flood and drought management strategies.

Modeling of microwave‐ and ultrasound‐ohmic‐assisted hydro‐distillation extraction of the Pimpinella anisum essential oil

AbstractFirst‐order, second‐order, sigmoid, and absorption models were used to predict the extraction yield (EY) of anise essential oil (AEO). Sigmoid model was able to predict the EY with R2 0.9852 and 0.9869 respectively for ohmic‐assisted hydro‐distillation methods with ultrasound and microwave pretreatments. It was found that among the different prediction models, adaptive neuro‐fuzzy inference system (ANFIS) has the highest accuracy for EY estimating. So that a network with the help of Mamdani's maximum‐minimum method and triangular membership function was able to predict the EY in both pretreatments with R2 above 0.99. The results of artificial neural network (ANN) modeling showed that the multilayer perceptron network with feed‐forward back propagation structure, Levenberg–Marquardt training algorithm, and with configurations 3‐16‐7‐1 and 3‐14‐5‐1 was able to have the best performance in EY predicting of ultrasound and microwave pretreatments, respectively. The results emphasize the successful use of models, especially dynamic models, in predicting the kinetics of essential oil extraction.Practical applicationsModeling helps to understand the basic process and is suitable for better control of the process and increasing its efficiency. Mathematical models, as a relatively simple method, lead to a better understanding of the mechanism and factors affecting extraction processes. Although mathematical models have many advantages in identifying and predicting the behavior of parameters in different conditions, generally, they are not very accurate in predicting complex behaviors. Dynamic modeling including artificial neural networks (ANNs) and fuzzy logic has recently received much attention due to its ability to learn complex processes and predict nonlinear relationships. The results emphasize the successful use of models, especially dynamic models, in predicting the kinetics of essential oil extraction.

Performance prediction of current-voltage characteristics of Schottky diodes at low temperatures using artificial intelligence

Schottky diodes are still one of the most important elements of electronics. Therefore, investigating the properties of diodes is very important in determining their usage areas. In this study, the performance of the artificial neural network model trained using high temperature data in predicting the current-voltage properties at low temperatures was investigated. An artificial neural network is modeled using the experimentally measured current and voltage values at the temperature range of 80 and 375 K. In the developed network model, temperature and voltage values are defined as input parameters and current values are estimated. Levenberg-Marquardt training algorithm was used as the training algorithm in the neural network, which was developed using a total of 1584 data. The current values obtained from the artificial neural network were compared with the experimental current values, and the prediction performance of the network model was extensively analyzed by using various performance parameters. The results showed that the developed artificial neural network can predict current values at low temperatures with high accuracy depending on voltage. In addition, it was found that the current-voltage characteristics of the Schottky diode at low temperatures could be predicted with an error rate of approximately ±7 %. On the other hand, the error rates in the prediction of diode characteristics by artificial intelligence were determined to be independent of temperature.

China mainland new energy index price forecasting with the neural network

For policymakers and investors, forecasting prices of energy indices has always been an important task. The present work focuses on the Chinese market and explores the daily price forecasting problem for the new energy index in the mainland during the period spanning January 4, 2016 – December 31, 2020. Our analysis is facilitated through the nonlinear autoregressive neural network model and one hundred and twenty model settings are tested in the fields of the algorithm for training the model, the number of hidden neurons utilized, the number of delays utilized, and the ratio utilized for segmenting the price series into different phases. Analysis here leads to the construction of a rather simple model based upon four delays and two hidden neurons with the Levenberg-Marquardt algorithm for training, which generates accurate and stable forecast results, with relative root mean square errors below 1.80% and mean absolute percentage errors below 1.30% across training, validation, and testing phases and for the overall sample. This constructed model also leads to statistically significantly better forecasting performance than a linear autoregressive model at the 1% significance level based upon the modified Diebold-Mariano test. The model built could be used as part of policy analysis for policymakers and decision making for investors. The forecasting results might also benefit design of similar energy indices by offering reference information in terms of price paths projected through the model.

Artificial neural network (ANN) modeling for simultaneous removal of a binary mixture of Pb(II) and Cu(II) by cobalt hydroxide nano‐flakes

AbstractA three‐layer artificial neural network (ANN) model was developed to predict the efficiency of Cu(II) and Pb(II) ion removal from aqueous solution by cobalt hydroxide nano‐flakes. It is based on experimental sets obtained from a D‐optimal design. The input variables to the neural network were as follows: the initial concentration of Pb(II) and Cu (II) ions (mg L−1), initial pH, and sorbent mass (g). The configuration of the backpropagation neural network for both Cu(II) and Pb (II) ions was a tangent sigmoid transfer function (tansig) at the hidden layer, linear transfer function (purelin) at the output layer, and Levenberg–Marquardt training algorithm (LMA). ANN‐predicted results were very close to the experimental results with a coefficient of determination (R2) of 0.9970 and mean square error (MSE) 0.000376. Analysis based on the ANN model indicated that sorbent mass appeared to be the most influential factor in the adsorption process of Cu(II) and Pb(II). Characterization of the cobalt hydroxide nano‐flakes and possible metal ions‐adsorbent interactions were confirmed by Fourier transform infrared spectroscopy (FT‐IR), X‐ray diffraction (XRD), and scanning electron microscopy (SEM).

Prediction of chamomile essential oil yield (Matricaria chamomilla L.) by physicochemical characteristics of soil

The purpose of this study was to predict the percentage and yield of chamomile essential oils using the artificial neural network system based on some soil physicochemical properties. Several habitats of chamomile cultivation were investigated and 100 soil samples were shipped to the greenhouse. The maximum and minimum of pH, EC, K, OM (organic matter), CCE (calcium carbonate equivalent), and clay in soils were 8.75-7.94, 1.6-1.0, 381-135, 2.30-0.22, 69-16, and 55.6-32.0, respectively. Growth indices, essential oil percentage, and yield were measured. Artificial neural network modeling was carried out to predict the essential oil concentration and yield using three groups of soil properties as a predictor: 1- nitrogen (N), phosphorus (P), potassium (K), and clay; 2- pH, EC, organic matter (OM) and clay; 3- CCE, clay, silt, sand, N, P, K, OM, pH, and EC. So, three pedotransfer functions (PTFs) were developed using the multi-layer perceptron (MPL) with Levenberg-Marquardt training algorithm for estimating chamomile essential oil content. Results evaluation of the accuracy and reliability of showed that, the third PTF (PTF3) which developed by all independent variables had the highest accuracy and reliability. Results also showed that, it is possible to predict the concentration and yield of chamomile essential oil based on soil physicochemical properties. This issue is important in terms of land suitability, identify areas susceptible to chamomile cultivation and planning for essential oil yields.

AI Method for Improving Crop Yield Prediction Accuracy Using ANN

Crop Yield Prediction (CYP) is critical to world food production. Food safety is a top priority for policymakers. They rely on reliable CYP to make import and export decisions that must be fulfilled before launching an agricultural business. Crop Yield (CY) is a complex variable influenced by multiple factors, including genotype, environment, and their interactions. CYP is a significant agrarian issue. However, CYP is the main task due to many composite factors, such as climatic conditions and soil characteristics. Machine Learning (ML) is a powerful tool for supporting CYP decisions, including decision support on which crops to grow in a specific season. Generally, Artificial Neural Networks (ANN) are usually used to predict the behaviour of complex non-linear models. As a result, this research paper attempts to determine the correlations between climatic variables, soil nutrients, and CY with the available data. In ANN, three methods, Levenberg-Marquardt (LM), Bayesian regularisation (BR), and scaled conjugate gradient (SCG), are used to train the neural network (NN) model and then compared to determine prediction accuracy. The performance measures of the training, as declared above, such as Mean Squared Error (MSE) and correlation coefficient (R), were determined to assess the ANN models that had been built. The experimental study proves that LM training algorithms are better, while BR and SCG have minimal performance.

Optimal battery state of charge parameter estimation and forecasting using non-linear autoregressive exogenous

The lithium-ion battery (LiB) has become the most widely used energy storage system for electric vehicles (EVs) due to its many advantages. The EV battery pack needs a battery management system (BMS) to estimate the state of charge (SOC) and balance the energy capacity through the cells. Apart from the fact that it is still challenging to accurately solve, the SOC forecasting represents an important concern in the study sector. This research proposes an effective battery SOC forecasting approach utilizing the non-linear autoregressive exogenous model (NARX) time’s series optimized Levenberg-Marquardt training algorithm, and Bayesian-Regularization (BR). The suggested technique is well-known for its resilience and high performance in nonlinear and complex system prediction, and it is extensively used in a wide range of disciplines. Also, the precision of the NARX technique has been investigated as a function of training data sets, error classifications based on experimental data of LiB. Both algorithms were evaluated with experimental data. Discharging followed by resting process was conducted on a 2.6 Ah LiB. They demonstrate good convergence in the low error and regression. In an effort to address a gap in the field, this paper offers a comparison between NARX-LM and NARX-BR algorithms for the LiB SOC prediction. Both algorithms are optimized the ANN using times series analysis based in the same training data. The results show that NARX-BR is more rapid and accurate with a low mean square error (MSE) of 2.39 10-5 than NARX-LM, which achieved an MSE of 1.11. Thus, it shows NARX-BR as an effective technique for LiB SOC prediction.

Modelling and parameter identification of coefficient of friction for deep-drawing quality steel sheets using the CatBoost machine learning algorithm and neural networks

The development of models for the coefficient of friction is difficult due to many factors influencing its value and many tribological phenomena that accompany contact between metals (i.e., flattening, ploughing, adhesion), the influence of which also depends on the friction conditions. Therefore, developing an analytical model of friction is difficult. In this article, the CatBoost machine learning algorithm, newly developed by Yandex researchers and engineers, is used for modelling and parameter identification of friction coefficients for three grades of deep-drawing quality steel sheets. Experimental tests to determine the friction coefficient were carried out using the strip drawing method with the use of a specially designed tribological device. Lubrication conditions, normal force, and the surface roughness of countersample surfaces were used as input parameters. The friction tests were conducted in dry friction and lubricated conditions with three grades of oils with a wide range of viscosities. Different transfer functions and various training algorithms were tested to build the optimal structure of the artificial neural networks. An analytical equation based on the parameters that were being investigated was created to calculate the COF of each material. Different methods of partitioning weight were employed for the expected COF to assess the relative importance (RI) and individual feature’s relevance. A Shapley decision plot, which uses cumulative Shapley additive explanations (SHAP) values, was used to depict models for predicting COF. CatBoost was able to predict the coefficient of friction with R2 values between 0.9547 and 0.9693 as an average for the training and testing dataset, depending on the grade of steel sheet. When considering all the materials that were tested, it was discovered that the Levenberg–Marquardt training algorithm performed the best in predicting the coefficient of friction.

Increasing the accuracy of estimating the viscosity of SAE40-based nanofluid containing MWCNT-TiO2 nanoparticles using a creative method in optimizing the structure of the artificial neural network

The viscosity (μnf) is one of the influencing parameters in choosing that nanofluid (NF) that affects its thermal behavior and heat transfer. In this regard, the present study is conducted to investigate the μnfof MWCNT-TiO2 (10:90) /SAE40 NF using an artificial neural network (ANN). ANN design in temperature conditions between 25 and 50°C and in different solid volume fraction (SVF) of nanoparticles (φ =0.0625%−1%). 174 laboratory data were used. Three inputs (temperature(T), φ and shear rate(SR)) and one output (μnf) are determined for ANN. In this study, ANN modeling was done with MLP method and Levenberg-Marquardt (LM) training algorithm. The selected optimal structure, among different ANN structures for MWCNT-TiO2(10:90)/SAE40 NF, has two hidden layers with an optimal structure of 10 and 4 neurons in the first and second layers. The results of R and MSE coefficients prove the accuracy of the proposed model., which in the final stage was set equal to 0.9999507 and 0.004599708, respectively. The margin of deviation (MOD) in the grid data set is in the range − 3% <MOD < + 3%. Based on studies that considered ANN correlation with computational data compared to laboratory data, the results of this comparison show that the ANN is more accurate and reliable for estimating the μnf. The turning point of this article is designing and predicting the viscosity of MWCNT-TiO2/SAE40 NF in the least time and financial costs compared to repetitive and time-consuming experiments through ANN.